Question

A pure Si semiconductor is doped with As. If the number of electrons are 10²0 per m³, find the number of holes. (given that n_t = 1.5 × 10¹⁶ m^-3)
1. 1.5 × 10⁴ m-3
2. 2.5 × 1010 m-3
3. 5 × 108 m-3
4. 2.25 × 1012 m-3

Answer 1

Correct Answer - Option 4 : 2.25 × 1012 m-3

CONCEPT:

In a semiconductor, the holes and electrons concentration in thermal equilibrium is given by:

\(n_e \times n_h=n_t^2\)

where n_e is the number of electrons, n_h is the number of holes, and n_t is the thermally generated electrons.

CALCULATION:

Given that n_e = 1020 per m3, and nt = 1.5 × 1016 m-3

We know that 

\(n_e \times n_h=n_t^2\)

\( 10^{20} \times n_h=(1.5 \times 10^{16})^2\)

nh = 2.25 × 10¹2 m-3

So the correct answer is option 4.